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MAHATRANSCO MCQs

Practice MAHATRANSCO-oriented Electronics & Telecommunication Engineering MCQs with answers and explanations for technical exam preparation. Questions are arranged in pages of up to 100.

Question 1601

Network TheoryNetwork Synthesis

A real-rational function F(s) is called positive real if, among other requirements, Re[F(s)] is?

ANonnegative for Re(s)>0
BAlways negative for Re(s)>0
CZero for every complex s
DInfinite on the entire j-omega axis

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Correct Answer: A. Nonnegative for Re(s)>0

Explanation: One defining condition of a positive-real function is Re[F(s)]>=0 in the open right-half s-plane, together with appropriate real-rational symmetry conditions.

Reference: Standard network theory: positive-real condition

Question 1602

Network TheoryNodal Analysis

In modified nodal analysis, an ideal voltage source connected between two non-reference nodes is commonly handled by introducing?

AAn additional source-current unknown and a voltage constraint equation
BAn open circuit in every case
CA short circuit in every case
DOnly a mesh-current equation with no node voltages

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Correct Answer: A. An additional source-current unknown and a voltage constraint equation

Explanation: Modified nodal analysis augments the node-voltage equations with an unknown current through the voltage source and an equation enforcing the source voltage.

Reference: Standard network theory: modified nodal analysis

Question 1603

Network TheoryNodal Analysis

A supernode is formed in nodal analysis when an ideal voltage source is connected between?

ATwo non-reference nodes
BA node and a resistor only
CTwo current sources in series
DTwo reference nodes only

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Correct Answer: A. Two non-reference nodes

Explanation: A voltage source between two unknown-voltage nodes prevents direct branch-current expression by conductance, so the two nodes are treated together as a supernode.

Reference: Standard network theory: supernode

Question 1604

Network TheoryNodal Analysis

Two non-reference nodes V1 and V2 are connected by an ideal 5 V source with V1 positive relative to V2. The required voltage constraint is?

AV1+V2=5
BV1-V2=5
CV2-V1=5
DV1V2=5

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Correct Answer: B. V1-V2=5

Explanation: The stated polarity means V1 is 5 V higher than V2, hence V1-V2=5 V.

Reference: Standard network theory: supernode constraint

Question 1605

Network TheoryMesh Analysis

A supermesh is used in mesh analysis when an ideal current source lies in a branch common to?

ATwo adjacent meshes
BA mesh and the reference node only
CTwo voltage sources in parallel
DTwo resistors in series only

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Correct Answer: A. Two adjacent meshes

Explanation: A current source shared by adjacent meshes prevents writing an ordinary KVL equation through that branch, so the surrounding meshes are combined into a supermesh.

Reference: Standard network theory: supermesh

Question 1606

Network TheoryMesh Analysis

If a 3 A current source lies in the common branch of mesh currents I1 and I2 and its direction corresponds to I1-I2, the mesh-current constraint is?

AI1+I2=3
BI1-I2=3
CI2-I1=0
DI1I2=3

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Correct Answer: B. I1-I2=3

Explanation: With the specified direction convention, the branch current is I1-I2, and the current source fixes this difference at 3 A.

Reference: Standard network theory: supermesh constraint

Question 1607

Network TheoryCoupled Circuits

Two magnetically coupled coils have L1=4 H, L2=9 H, and coupling coefficient k=0.5. Their mutual inductance M is?

A1.5 H
B3 H
C6 H
D18 H

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Correct Answer: B. 3 H

Explanation: M=k sqrt(L1L2)=0.5×sqrt(4×9)=0.5×6=3 H.

Reference: Standard network theory: mutual inductance numerical

Question 1608

Network TheoryCoupled Circuits

The coefficient of coupling k between two passive coupled coils normally lies in the range?

A0 to 1
B1 to 10
C-10 to 10 only
DGreater than 1

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Correct Answer: A. 0 to 1

Explanation: The magnitude of coupling coefficient is bounded by 0<=k<=1, where k=1 represents ideal complete coupling.

Reference: Standard network theory: coefficient of coupling

Question 1609

Network TheoryCoupled Circuits

For two coupled inductors connected in series aiding, the equivalent inductance is?

AL1+L2-2M
BL1+L2+2M
CL1L2/M
DM-L1-L2

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Correct Answer: B. L1+L2+2M

Explanation: With series-aiding polarity, mutual flux reinforces self flux, giving Leq=L1+L2+2M.

Reference: Standard network theory: series-aiding coupled coils

Question 1610

Network TheoryNetwork Synthesis

In a lossless LC driving-point reactance function, poles and zeros on the j-omega axis characteristically?

AInterlace
BAlways coincide
COccur only at positive real s
DHave no ordering relationship

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Correct Answer: A. Interlace

Explanation: For realizable LC reactance functions, simple poles and zeros lie on the imaginary axis and alternate, or interlace, with frequency.

Reference: Standard network theory: reactance functions

Question 1611

Network TheoryNetwork Synthesis

Foster’s first form for an LC driving-point impedance is obtained from a partial-fraction expansion of?

AThe impedance function Z(s)
BOnly the time-domain current
CThe incidence matrix
DThe nodal determinant only

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Correct Answer: A. The impedance function Z(s)

Explanation: Foster-I impedance realization follows directly from expanding Z(s) into partial fractions, with terms represented by simple reactive sections.

Reference: Standard network theory: Foster realization

Question 1612

Network TheoryNetwork Synthesis

Cauer network synthesis is based primarily on?

AContinued-fraction expansion
BFourier-series expansion
CTaylor expansion around infinity only
DMatrix inversion without a network function

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Correct Answer: A. Continued-fraction expansion

Explanation: Cauer forms are ladder realizations derived by successive continued-fraction expansion of a driving-point impedance or admittance.

Reference: Standard network theory: Cauer realization

Question 1613

Network TheoryTwo-Port Networks

For z-parameters of a two-port network, the defining equations use port voltages as linear combinations of?

APort currents
BPort powers
COnly source voltages
DOnly load resistances

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Correct Answer: A. Port currents

Explanation: The z-parameter representation is V1=z11 I1+z12 I2 and V2=z21 I1+z22 I2.

Reference: Standard network theory: z-parameters

Question 1614

Network TheoryTwo-Port Networks

For a reciprocal two-port represented by z-parameters, which relation must hold?

Az11=z22
Bz12=z21
Cz11=z12
Dz21=0

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Correct Answer: B. z12=z21

Explanation: Reciprocity in the impedance-parameter representation requires the transfer impedances to be equal: z12=z21.

Reference: Standard network theory: reciprocal z-parameters

Question 1615

Network TheoryTwo-Port Networks

For a symmetrical two-port represented by z-parameters, which relation holds?

Az11=z22
Bz12=0
Cz21=0
Dz11=z12 always

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Correct Answer: A. z11=z22

Explanation: Symmetry means interchanging the two ports leaves the network behavior unchanged, which requires z11=z22.

Reference: Standard network theory: symmetrical z-parameters

Question 1616

Network TheoryTwo-Port Networks

For y-parameters of a two-port network, the port currents are expressed as linear combinations of?

APort voltages
BPort powers
COnly port impedances
DOnly source currents

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Correct Answer: A. Port voltages

Explanation: The admittance representation is I1=y11 V1+y12 V2 and I2=y21 V1+y22 V2.

Reference: Standard network theory: y-parameters

Question 1617

Network TheoryTwo-Port Networks

For a reciprocal two-port represented by y-parameters, reciprocity requires?

Ay11=y22
By12=y21
Cy11=0
Dy22=0

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Correct Answer: B. y12=y21

Explanation: For the standard y-parameter sign convention, a reciprocal network satisfies y12=y21.

Reference: Standard network theory: reciprocal y-parameters

Question 1618

Network TheoryTwo-Port Networks

The h-parameter h11 of a two-port is an input impedance measured with?

AOutput port short-circuited
BOutput port open-circuited
CInput port open-circuited
DBoth ports disconnected

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Correct Answer: A. Output port short-circuited

Explanation: From V1=h11 I1+h12 V2, setting V2=0 corresponds to an output short circuit, so h11=V1/I1 under that condition.

Reference: Standard network theory: h-parameters

Question 1619

Network TheoryTwo-Port Networks

The h-parameter h22 is an output admittance measured with?

AInput port open-circuited
BInput port short-circuited
COutput port open-circuited
DBoth port currents zero

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Correct Answer: A. Input port open-circuited

Explanation: From I2=h21 I1+h22 V2, setting I1=0 means the input port is open, so h22=I2/V2 under that condition.

Reference: Standard network theory: h-parameters

Question 1620

Network TheoryCoupled Circuits

Two identical uncoupled inductors of 4 H each are connected in series. Their equivalent inductance is?

A2 H
B4 H
C8 H
D16 H

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Correct Answer: C. 8 H

Explanation: For uncoupled inductors in series, inductances add: Leq=4+4=8 H.

Reference: Standard network theory: uncoupled inductors

Question 1621

Network TheoryCoupled Circuits

Two coupled coils have L1=2 H, L2=3 H and M=1 H. If connected in series opposing, their equivalent inductance is?

A1 H
B3 H
C5 H
D7 H

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Correct Answer: B. 3 H

Explanation: For series-opposing connection, Leq=L1+L2-2M=2+3-2=3 H.

Reference: Standard network theory: series-opposing coupled coils

Question 1622

Network TheoryTransient Analysis

A capacitor voltage just before switching is 12 V. If no impulsive current is applied at the switching instant, its voltage immediately after switching is?

A0 V
B6 V
C12 V
DInfinite

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Correct Answer: C. 12 V

Explanation: Capacitor voltage cannot change instantaneously without an impulse current, so vC(0+)=vC(0-)=12 V.

Reference: Standard network theory: capacitor continuity

Question 1623

Network TheoryTransient Analysis

An inductor carries 3 A just before switching. If no impulsive voltage is applied, its current immediately after switching is?

A0 A
B1.5 A
C3 A
DInfinite

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Correct Answer: C. 3 A

Explanation: Inductor current is continuous in the absence of an impulse voltage, hence iL(0+)=iL(0-)=3 A.

Reference: Standard network theory: inductor continuity

Question 1624

Network TheoryEnergy Storage

A 10 microfarad capacitor initially at 20 V stores how much energy?

A0.2 mJ
B1 mJ
C2 mJ
D4 mJ

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Correct Answer: C. 2 mJ

Explanation: Stored energy is W=0.5CV^2=0.5×10e-6×20^2=0.002 J=2 mJ.

Reference: Standard network theory: capacitor energy numerical

Question 1625

Network TheorySecond-Order Circuits

For a series RLC circuit with L=1 H and C=0.25 F, the undamped natural frequency omega0 is?

A0.5 rad/s
B1 rad/s
C2 rad/s
D4 rad/s

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Correct Answer: C. 2 rad/s

Explanation: omega0=1/sqrt(LC)=1/sqrt(1×0.25)=2 rad/s.

Reference: Standard network theory: natural frequency numerical

Question 1626

Network TheorySecond-Order Circuits

If a second-order network has alpha=2 rad/s and omega0=5 rad/s, its natural response is?

AOverdamped
BCritically damped
CUnderdamped
DNoncausal

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Correct Answer: C. Underdamped

Explanation: Since alpha<omega0, the characteristic roots are complex conjugates and the response is underdamped.

Reference: Standard network theory: damping classification

Question 1627

Network TheorySecond-Order Circuits

For an underdamped second-order network, the damped natural frequency omega_d equals?

Aalpha+omega0
Bsqrt(omega0^2-alpha^2)
Csqrt(alpha^2+omega0^2)
Domega0/alpha

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Correct Answer: B. sqrt(omega0^2-alpha^2)

Explanation: For alpha<omega0, the oscillatory frequency is omega_d=sqrt(omega0^2-alpha^2).

Reference: Standard network theory: damped natural frequency

Question 1628

Network TheorySecond-Order Circuits

If omega0=10 rad/s and alpha=6 rad/s, the damped natural frequency is?

A4 rad/s
B6 rad/s
C8 rad/s
D16 rad/s

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Correct Answer: C. 8 rad/s

Explanation: omega_d=sqrt(10^2-6^2)=sqrt(64)=8 rad/s.

Reference: Standard network theory: damped frequency numerical

Question 1629

Network TheoryLaplace Transform

The unilateral Laplace transform of the unit impulse delta(t) is?

A0
B1
C1/s
Ds

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Correct Answer: B. 1

Explanation: The unilateral Laplace transform of a unit impulse at t=0 is 1 under the standard engineering convention.

Reference: Standard network theory: impulse transform

Question 1630

Network TheoryEnergy Storage

A 2 H inductor carrying 4 A stores how much magnetic energy?

A4 J
B8 J
C16 J
D32 J

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Correct Answer: C. 16 J

Explanation: Inductor energy is W=0.5LI^2=0.5×2×4^2=16 J.

Reference: Standard network theory: inductor energy numerical

Question 1631

Network TheoryTransient Analysis

For a source-free RC circuit with R=20 kOhm and C=5 microfarad, the time constant is?

A10 ms
B50 ms
C100 ms
D500 ms

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Correct Answer: C. 100 ms

Explanation: tau=RC=20000×5e-6=0.1 s=100 ms.

Reference: Standard network theory: RC time constant numerical

Question 1632

Network TheoryTransient Analysis

In a first-order circuit, after approximately five time constants the transient term has fallen to about?

A36.8%
B13.5%
C5%
D0.67%

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Correct Answer: D. 0.67%

Explanation: The natural term is e^(-t/tau). At t=5tau, e^-5≈0.0067, or about 0.67% of its initial value.

Reference: Standard network theory: settling of first-order response

Question 1633

Network TheoryTransient Analysis

For a DC step V applied to an initially uncharged series RC circuit, the capacitor voltage is?

AV e^(-t/RC)
BV[1-e^(-t/RC)]
CV(1+t/RC)
DV sin(t/RC)

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Correct Answer: B. V[1-e^(-t/RC)]

Explanation: The charging response starts at zero and approaches V exponentially: vC(t)=V[1-e^(-t/RC)].

Reference: Standard network theory: RC step response

Question 1634

Network TheoryTransient Analysis

A 10 V DC step is applied to an initially uncharged RC circuit. After one time constant, the capacitor voltage is closest to?

A3.68 V
B5.00 V
C6.32 V
D10.0 V

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Correct Answer: C. 6.32 V

Explanation: At t=tau, vC=V(1-e^-1)≈0.632V=6.32 V.

Reference: Standard network theory: RC charging numerical

Question 1635

Network TheoryTransient Analysis

For a DC step V applied to a series RL circuit with zero initial current, the current approaches its final value according to?

A(V/R)[1-e^(-tR/L)]
B(V/R)e^(-tR/L)
CVLe^(-t)
D(R/V)[1-e^(-tL/R)]

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Correct Answer: A. (V/R)[1-e^(-tR/L)]

Explanation: The RL step current rises from zero to V/R with time constant L/R: i(t)=(V/R)[1-e^(-tR/L)].

Reference: Standard network theory: RL step response

Question 1636

Network TheoryTransient Analysis

A series RL circuit has L=2 H and R=10 ohm. Its time constant is?

A0.05 s
B0.2 s
C5 s
D20 s

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Correct Answer: B. 0.2 s

Explanation: For an RL circuit, tau=L/R=2/10=0.2 s.

Reference: Standard network theory: RL time constant numerical

Question 1637

Network TheorySecond-Order Circuits

A series RLC natural response is critically damped when the damping factor alpha and undamped natural frequency omega0 satisfy?

Aalpha=0
Balpha<omega0
Calpha=omega0
Dalpha>omega0

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Correct Answer: C. alpha=omega0

Explanation: Critical damping occurs at the boundary between underdamped and overdamped responses, where alpha=omega0.

Reference: Standard network theory: critical damping

Question 1638

Network TheorySecond-Order Circuits

A series RLC circuit has R=4 ohm and L=1 H. Its damping factor alpha is?

A1 rad/s
B2 rad/s
C4 rad/s
D8 rad/s

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Correct Answer: B. 2 rad/s

Explanation: For a series RLC circuit, alpha=R/(2L)=4/(2×1)=2 rad/s.

Reference: Standard network theory: damping factor numerical

Question 1639

Network TheoryLaplace Transform

The Laplace transform of t for t>=0 is?

A1/s
B1/s^2
Cs
Ds^2

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Correct Answer: B. 1/s^2

Explanation: Using L{t^n}=n!/s^(n+1), for n=1 the transform is 1/s^2.

Reference: Standard network theory: transform of ramp

Question 1640

Network Theorys-Domain Circuits

The Laplace-domain impedance of an initially relaxed inductor is?

A1/(sL)
BsL
CL/s
Ds/L

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Correct Answer: B. sL

Explanation: With zero initial current, V(s)=sL I(s), so the inductor impedance is ZL(s)=sL.

Reference: Standard network theory: inductor s-domain impedance

Question 1641

Network Theorys-Domain Circuits

The Laplace-domain impedance of an initially relaxed capacitor is?

AsC
B1/(sC)
CC/s
Ds/C

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Correct Answer: B. 1/(sC)

Explanation: With zero initial voltage, I(s)=sC V(s), hence ZC(s)=V/I=1/(sC).

Reference: Standard network theory: capacitor s-domain impedance

Question 1642

Network TheoryNetwork Functions

A transfer function has a zero at s=-4. Which factor appears in its numerator?

As-4
Bs+4
C1/(s+4)
Ds^2+4

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Correct Answer: B. s+4

Explanation: A zero at s=-4 means the numerator becomes zero at -4, so it contains the factor (s+4).

Reference: Standard network theory: zeros

Question 1643

Network TheoryNetwork Functions

A stable causal rational network function requires all natural-response poles to lie where in the s-plane?

AOpen right-half plane
BOpen left-half plane
COnly at the origin
DAnywhere on the real axis

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Correct Answer: B. Open left-half plane

Explanation: For asymptotic stability of a causal continuous-time rational network, natural modes must decay, requiring poles in the open left-half plane.

Reference: Standard network theory: stability and poles

Question 1644

Network TheoryNetwork Functions

A pole located at s=-50 corresponds to an exponential natural mode with time constant?

A0.002 s
B0.02 s
C0.05 s
D50 s

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Correct Answer: B. 0.02 s

Explanation: A pole at -1/tau=-50 gives tau=1/50=0.02 s.

Reference: Standard network theory: pole and time constant

Question 1645

Network TheoryNetwork Functions

For H(s)=(s+2)/[(s+5)(s+10)], the finite zero is located at?

As=-10
Bs=-5
Cs=-2
Ds=+2

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Correct Answer: C. s=-2

Explanation: The numerator becomes zero when s+2=0, so the finite zero is at s=-2.

Reference: Standard network theory: pole-zero identification

Question 1646

Network TheoryTwo-Port Networks

When two two-port networks are connected in parallel at both ports, which parameter matrices are especially convenient to add directly?

Az-parameters
By-parameters
CABCD parameters
Dh-parameters only

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Correct Answer: B. y-parameters

Explanation: For parallel-connected two-ports, corresponding port voltages are common and currents add, making admittance or y-parameters convenient.

Reference: Standard network theory: parallel two-port connection

Question 1647

Network TheoryTwo-Port Networks

When two two-port networks are connected in series at both ports, which parameter matrices are especially convenient to add directly?

Az-parameters
By-parameters
CABCD parameters
DS-parameters only

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Correct Answer: A. z-parameters

Explanation: In a series-series interconnection, port currents are common and voltages add, so impedance or z-parameter matrices add directly.

Reference: Standard network theory: series two-port connection

Question 1648

Network TheoryTwo-Port Networks

For two cascaded two-port networks, which representation is normally the most convenient because the overall matrix is obtained by ordered multiplication?

Az-parameters
By-parameters
CABCD parameters
Dg-parameters

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Correct Answer: C. ABCD parameters

Explanation: Transmission or ABCD matrices multiply directly in cascade order, which makes them convenient for cascaded networks.

Reference: Standard network theory: cascaded two-port representation

Question 1649

Network TheoryTwo-Port Networks

In a two-port network described by inverse-hybrid or g-parameters, the independent variables are?

AV1 and I2
BI1 and V2
CV1 and V2
DI1 and I2

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Correct Answer: A. V1 and I2

Explanation: The g-parameter form uses I1=g11V1+g12I2 and V2=g21V1+g22I2, so V1 and I2 are the independent variables.

Reference: Standard network theory: inverse-hybrid parameters

Question 1650

Network TheoryTwo-Port Networks

For a reciprocal two-port represented by h-parameters, the reciprocity condition is?

Ah12=h21
Bh12=-h21
Ch11=h22
Dh11h22=1

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Correct Answer: B. h12=-h21

Explanation: With the standard hybrid-parameter convention, reciprocity requires h12=-h21.

Reference: Standard network theory: reciprocal h-parameters

Question 1651

Network TheoryTwo-Port Networks

For a symmetrical two-port represented by ABCD parameters, which condition is required?

AA=D
BB=C
CA=B
DC=D

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Correct Answer: A. A=D

Explanation: Symmetry of a two-port in transmission parameters requires A=D.

Reference: Standard network theory: symmetrical ABCD parameters

Question 1652

Network TheoryTwo-Port Networks

A transmission line section represented by ABCD parameters has A=2, B=3 ohm, C=1 siemens and D=2. Is it reciprocal?

AYes, because AD-BC=1
BNo, because AD-BC=7
CYes, because A=D
DNo, because B is not equal to C

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Correct Answer: A. Yes, because AD-BC=1

Explanation: For reciprocity, AD-BC must equal 1. Here 2×2-3×1=1, so the network satisfies the reciprocity condition.

Reference: Standard network theory: ABCD reciprocity numerical

Question 1653

Network TheoryCoupled Circuits

An ideal transformer has turns ratio N1/N2=4. A 100 ohm load connected to the secondary is reflected to the primary as?

A6.25 ohm
B25 ohm
C400 ohm
D1600 ohm

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Correct Answer: D. 1600 ohm

Explanation: The reflected impedance is Zp=(N1/N2)^2 ZL=4^2×100=1600 ohm.

Reference: Standard network theory: transformer impedance reflection

Question 1654

Network TheoryCoupled Circuits

An ideal transformer has N1/N2=5 and primary voltage 250 V RMS. The secondary voltage magnitude is?

A10 V
B50 V
C250 V
D1250 V

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Correct Answer: B. 50 V

Explanation: For an ideal transformer, V1/V2=N1/N2=5, so V2=250/5=50 V.

Reference: Standard network theory: ideal transformer voltage ratio

Question 1655

Network TheoryCoupled Circuits

For an ideal transformer with N1/N2=5, if the secondary current is 10 A, the primary current magnitude is?

A2 A
B5 A
C10 A
D50 A

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Correct Answer: A. 2 A

Explanation: For an ideal transformer, I1/I2=N2/N1=1/5, hence I1=10/5=2 A.

Reference: Standard network theory: ideal transformer current ratio

Question 1656

Network TheoryCoupled Circuits

If the dot convention shows current entering the dotted terminal of coil 1 and the mutually induced voltage of coil 2 is referenced positive at its dotted terminal, the mutual-voltage term is taken as?

A+M di1/dt
B-M di1/dt
CZero for all coupling
DM/i1

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Correct Answer: A. +M di1/dt

Explanation: With the stated dot-reference convention, current entering a dotted terminal induces a voltage positive at the dotted terminal of the other coil, giving a positive mutual term.

Reference: Standard network theory: dot convention

Question 1657

Network TheoryCoupled Circuits

Two coils have mutual inductance M=0.2 H. If current in coil 1 changes at 5 A/s, the magnitude of the mutually induced voltage in coil 2 is?

A0.04 V
B0.2 V
C1 V
D25 V

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Correct Answer: C. 1 V

Explanation: The magnitude is |v2|=M|di1/dt|=0.2×5=1 V.

Reference: Standard network theory: mutual induced voltage numerical

Question 1658

Network TheoryCoupled Circuits

For two coupled inductors, the maximum physically possible mutual inductance magnitude is?

AL1+L2
Bsqrt(L1L2)
CL1L2
D|L1-L2|

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Correct Answer: B. sqrt(L1L2)

Explanation: Since |k|<=1 and M=k sqrt(L1L2), the maximum magnitude of M is sqrt(L1L2).

Reference: Standard network theory: mutual inductance limit

Question 1659

Network TheoryNetwork Functions

A network function H(s)=(s+3)/(s^2+5s+6) has poles at?

A-1 and -6
B-2 and -3
C+2 and +3
D-3 only

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Correct Answer: B. -2 and -3

Explanation: The denominator factors as (s+2)(s+3), so the poles are at s=-2 and s=-3.

Reference: Standard network theory: pole calculation

Question 1660

Network TheoryNetwork Functions

For H(s)=(s+3)/[(s+2)(s+3)], exact pole-zero cancellation reduces the algebraic expression to?

A1/(s+2)
B1/(s+3)
Cs+2
Ds+3

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Correct Answer: A. 1/(s+2)

Explanation: The common factor (s+3) cancels algebraically, leaving H(s)=1/(s+2), subject to the usual caveat that internal system behavior may require separate consideration.

Reference: Standard network theory: pole-zero cancellation

Question 1661

Network TheoryNetwork Functions

A rational network function is strictly proper when?

ADegree of numerator is less than degree of denominator
BDegree of numerator equals degree of denominator
CDegree of numerator is greater than degree of denominator
DIts denominator is a constant

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Correct Answer: A. Degree of numerator is less than degree of denominator

Explanation: A strictly proper rational function has numerator degree lower than denominator degree, so its magnitude tends to zero as |s| tends to infinity.

Reference: Standard network theory: proper network functions

Question 1662

Network TheoryNetwork Functions

For H(s)=(2s+5)/(s+4), the high-frequency gain limit as |s| tends to infinity is?

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Correct Answer: C. 2

Explanation: For numerator and denominator of equal degree, the high-frequency limit is the ratio of leading coefficients, 2/1=2.

Reference: Standard network theory: high-frequency gain

Question 1663

Network TheoryNetwork Functions

The impulse response of a causal LTI network is obtained from its transfer function H(s) by?

ATaking the inverse Laplace transform of H(s)
BDifferentiating H(s) only with respect to resistance
CSetting s=0 only
DTaking the square of H(s)

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Correct Answer: A. Taking the inverse Laplace transform of H(s)

Explanation: For zero initial conditions, the causal impulse response h(t) is the inverse Laplace transform of H(s).

Reference: Standard network theory: impulse response

Question 1664

Network TheoryNetwork Functions

If H(s)=1/(s+4), the causal impulse response is?

Ae^(-4t)u(t)
B4e^(-t)u(t)
C1-e^(-4t)
Ddelta(t-4)

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Correct Answer: A. e^(-4t)u(t)

Explanation: The inverse Laplace transform of 1/(s+a) is e^(-at)u(t), so h(t)=e^(-4t)u(t).

Reference: Standard network theory: impulse response numerical

Question 1665

Network TheoryNetwork Functions

For zero initial conditions, the output transform of an LTI network with transfer function H(s) and input X(s) is?

AY(s)=H(s)+X(s)
BY(s)=H(s)X(s)
CY(s)=H(s)/X(s)
DY(s)=X(s)-H(s)

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Correct Answer: B. Y(s)=H(s)X(s)

Explanation: By definition of the transfer function under zero initial conditions, H(s)=Y(s)/X(s), hence Y(s)=H(s)X(s).

Reference: Standard network theory: transfer function input-output relation

Question 1666

Network TheoryNetwork Functions

A unit-step input has Laplace transform 1/s. For H(s)=5/(s+5), the output transform is?

A5/(s+5)
B1/[s(s+5)]
C5/[s(s+5)]
Ds/(s+5)

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Correct Answer: C. 5/[s(s+5)]

Explanation: Y(s)=H(s)X(s)=[5/(s+5)](1/s)=5/[s(s+5)].

Reference: Standard network theory: step response in s-domain

Question 1667

Network TheoryNetwork Functions

For H(s)=5/(s+5) excited by a unit step, the final output value is?

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Correct Answer: B. 1

Explanation: Using the final-value theorem, y(infinity)=lim(s->0) s·5/[s(s+5)]=5/5=1.

Reference: Standard network theory: step final value

Question 1668

Network TheoryNetwork Functions

The convolution integral for the zero-state output of a continuous-time LTI network is?

Ay(t)=integral x(tau)h(t-tau)d tau
By(t)=x(t)+h(t)
Cy(t)=x(t)/h(t)
Dy(t)=dx(t)/dt only

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Correct Answer: A. y(t)=integral x(tau)h(t-tau)d tau

Explanation: The zero-state response of an LTI system is the convolution of the input x(t) with the impulse response h(t).

Reference: Standard network theory: convolution

Question 1669

Network TheoryNetwork Functions

If x(t)=delta(t) is applied to an LTI network with impulse response h(t), the zero-state output is?

A0
B1
Ch(t)
DIntegral of h(t) only

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Correct Answer: C. h(t)

Explanation: The delta function is the identity element of convolution: delta(t)*h(t)=h(t).

Reference: Standard network theory: impulse input

Question 1670

Network TheoryNetwork Functions

For two causal LTI networks with transfer functions H1(s)=1/(s+1) and H2(s)=2/(s+3) connected in cascade, the overall transfer function is?

A3/(2s+4)
B2/[(s+1)(s+3)]
C2/(s+4)
D1/[(s+1)+(s+3)]

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Correct Answer: B. 2/[(s+1)(s+3)]

Explanation: Transfer functions multiply in cascade, so H(s)=H1(s)H2(s)=2/[(s+1)(s+3)].

Reference: Standard network theory: cascade transfer functions

Question 1671

Network TheoryNetwork Topology

In a connected planar graph with n nodes and b branches, the number of independent meshes is?

An-1
Bb-n+1
Cb+n-1
Db-1

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Correct Answer: B. b-n+1

Explanation: For a connected planar network, the number of independent meshes is b-n+1.

Reference: Standard network theory: planar graph topology

Question 1672

Network TheoryNetwork Topology

A connected network graph has 7 nodes and 11 branches. How many independent cut-set equations can be formed from a tree?

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Correct Answer: B. 6

Explanation: A tree of a connected graph has n-1 twigs, and each twig defines one fundamental cut-set. Thus 7-1=6.

Reference: Standard network theory: fundamental cut-set count

Question 1673

Network TheoryNetwork Topology

For an oriented graph, each column of the node-branch incidence matrix corresponding to an ordinary branch contains?

AOne +1 and one -1
BTwo +1 entries only
COne nonzero entry only
DAll zero entries

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Correct Answer: A. One +1 and one -1

Explanation: An oriented branch leaves one node and enters another, so its incidence-matrix column has one +1 and one -1 under a consistent sign convention.

Reference: Standard network theory: incidence matrix structure

Question 1674

Network TheoryNetwork Topology

If one row is deleted from the incidence matrix of a connected graph, the resulting reduced incidence matrix has how many rows for n nodes?

An
Bn-1
Cb-n+1
Db

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Correct Answer: B. n-1

Explanation: Deleting the dependent reference-node row leaves a reduced incidence matrix with n-1 rows.

Reference: Standard network theory: reduced incidence matrix

Question 1675

Network TheoryNetwork Topology

A tie-set matrix is primarily used to express branch currents in terms of?

AIndependent loop currents
BNode voltages only
CBranch powers
DCut-set voltages only

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Correct Answer: A. Independent loop currents

Explanation: Tie-set or fundamental-loop analysis relates branch currents to a set of independent loop currents.

Reference: Standard network theory: tie-set matrix

Question 1676

Network TheoryNetwork Topology

A cut-set matrix is particularly associated with writing independent forms of?

AKCL equations
BKVL equations only
CPower equations only
DTransformer equations

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Correct Answer: A. KCL equations

Explanation: Cut-set equations express current conservation across cuts of a graph and therefore provide independent KCL relations.

Reference: Standard network theory: cut-set matrix

Question 1677

Network TheorySource Transformation

A network has a 12 V ideal voltage source in series with 3 ohm. Its equivalent Norton current is?

A2 A
B3 A
C4 A
D36 A

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Correct Answer: C. 4 A

Explanation: Source transformation gives IN=V/R=12/3=4 A, with the same 3 ohm resistance in parallel.

Reference: Standard network theory: source transformation numerical

Question 1678

Network TheorySource Transformation

A Norton source of 5 A in parallel with 8 ohm is transformed to a Thevenin source of?

A5 V in series with 8 ohm
B13 V in series with 8 ohm
C40 V in series with 8 ohm
D40 V in series with 1.6 ohm

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Correct Answer: C. 40 V in series with 8 ohm

Explanation: Vth=IN RN=5×8=40 V and Rth=RN=8 ohm.

Reference: Standard network theory: Norton to Thevenin numerical

Question 1679

Network TheoryNetwork Theorems

For a linear circuit containing several independent sources, superposition is applied to calculate?

AVoltages and currents, not power directly
BPower directly by adding individual source powers at an element
CEquivalent resistance only
DFrequency only

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Correct Answer: A. Voltages and currents, not power directly

Explanation: Superposition applies to linear response quantities such as voltage and current. Power is nonlinear in voltage/current and cannot generally be superposed directly.

Reference: Standard network theory: superposition limitation

Question 1680

Network TheoryNetwork Theorems

While applying superposition, an independent ideal voltage source that is not being considered is replaced by?

AAn open circuit
BA short circuit
CIts internal power rating
DA dependent source

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Correct Answer: B. A short circuit

Explanation: Setting an ideal independent voltage source to zero volts makes it a short circuit.

Reference: Standard network theory: superposition voltage-source suppression

Question 1681

Network TheoryCircuit Analysis

A 20 V source is connected to two series resistors of 4 ohm and 6 ohm. The voltage across the 6 ohm resistor is?

A8 V
B10 V
C12 V
D15 V

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Correct Answer: C. 12 V

Explanation: By voltage division, V6=20×6/(4+6)=12 V.

Reference: Standard network theory: voltage divider numerical

Question 1682

Network TheoryCircuit Analysis

A total current of 10 A divides between parallel resistors 6 ohm and 3 ohm. The current through the 6 ohm branch is?

A2 A
B3.33 A
C5 A
D6.67 A

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Correct Answer: B. 3.33 A

Explanation: For two parallel resistors, current through 6 ohm is 10×3/(6+3)=3.33 A.

Reference: Standard network theory: current divider numerical

Question 1683

Network TheoryCircuit Analysis

Three resistors 2 ohm, 3 ohm and 6 ohm are connected in parallel. Their equivalent resistance is?

A1 ohm
B2 ohm
C3 ohm
D11 ohm

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Correct Answer: A. 1 ohm

Explanation: 1/Req=1/2+1/3+1/6=1, hence Req=1 ohm.

Reference: Standard network theory: parallel resistance numerical

Question 1684

Network TheoryCircuit Analysis

A 4 ohm resistor dissipates 36 W. The magnitude of current through it is?

A1.5 A
B3 A
C6 A
D9 A

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Correct Answer: B. 3 A

Explanation: Using P=I^2R, I=sqrt(36/4)=3 A.

Reference: Standard network theory: resistor power numerical

Question 1685

Network TheoryAC Circuit Analysis

A sinusoidal voltage has RMS value 230 V. Its peak value is approximately?

A162.6 V
B230 V
C325.3 V
D460 V

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Correct Answer: C. 325.3 V

Explanation: For a sinusoid, Vpeak=sqrt(2)Vrms≈1.414×230=325.3 V.

Reference: Standard network theory: RMS to peak numerical

Question 1686

Network TheoryAC Circuit Analysis

A sinusoidal current has peak value 10 A. Its RMS value is approximately?

A5 A
B7.07 A
C10 A
D14.14 A

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Correct Answer: B. 7.07 A

Explanation: For a sine wave, Irms=Ipeak/sqrt(2)=10/1.414≈7.07 A.

Reference: Standard network theory: peak to RMS numerical

Question 1687

Network TheoryAC Circuit Analysis

The average value of a pure sinusoidal voltage over one complete cycle is?

AIts RMS value
BIts peak value
CZero
DPeak divided by two

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Correct Answer: C. Zero

Explanation: Positive and negative half-cycle areas cancel, so the average over a full cycle is zero.

Reference: Standard network theory: sinusoidal average value

Question 1688

Network TheoryAC Circuit Analysis

For an impedance Z=3-j4 ohm, the magnitude of Z is?

A1 ohm
B5 ohm
C7 ohm
D25 ohm

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Correct Answer: B. 5 ohm

Explanation: |Z|=sqrt(3^2+(-4)^2)=5 ohm.

Reference: Standard network theory: complex impedance numerical

Question 1689

Network TheoryAC Circuit Analysis

For Z=3-j4 ohm, the impedance angle is closest to?

A-53.1 degrees
B+53.1 degrees
C-36.9 degrees
D+36.9 degrees

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Correct Answer: A. -53.1 degrees

Explanation: The angle is tan^-1(-4/3)≈-53.1 degrees, indicating capacitive behavior.

Reference: Standard network theory: impedance phase numerical

Question 1690

Network TheoryAC Circuit Analysis

An admittance is Y=0.04+j0.03 S. Its magnitude is?

A0.01 S
B0.05 S
C0.07 S
D0.12 S

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Correct Answer: B. 0.05 S

Explanation: |Y|=sqrt(0.04^2+0.03^2)=0.05 S.

Reference: Standard network theory: admittance magnitude numerical

Question 1691

Network TheoryAC Power

A load draws 10 A RMS from a 200 V RMS supply at power factor 0.6 lagging. Its real power is?

A600 W
B1200 W
C1600 W
D2000 W

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Correct Answer: B. 1200 W

Explanation: P=VI cos(phi)=200×10×0.6=1200 W.

Reference: Standard network theory: single-phase real power numerical

Question 1692

Network TheoryAC Power

For the same 200 V, 10 A, 0.6 lagging load, the reactive power magnitude is?

A800 var
B1200 var
C1600 var
D2000 var

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Correct Answer: C. 1600 var

Explanation: sin(phi)=sqrt(1-0.6^2)=0.8, so Q=VI sin(phi)=200×10×0.8=1600 var.

Reference: Standard network theory: single-phase reactive power numerical

Question 1693

Network TheoryNetwork Theorems

While applying superposition, an independent ideal current source that is not being considered is replaced by?

AA short circuit
BAn open circuit
CA voltage source of equal value
DA resistor of 1 ohm

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Correct Answer: B. An open circuit

Explanation: Setting an ideal independent current source to zero amperes makes it an open circuit.

Reference: Standard network theory: superposition current-source suppression

Question 1694

Network TheoryAC Power

A load consumes 3 kW and 4 kVAR. Its apparent power magnitude is?

A1 kVA
B5 kVA
C7 kVA
D12 kVA

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Correct Answer: B. 5 kVA

Explanation: |S|=sqrt(P^2+Q^2)=sqrt(3^2+4^2)=5 kVA.

Reference: Standard network theory: complex power triangle numerical

Question 1695

Network TheoryThree-Phase Circuits

A balanced three-phase delta-connected load has a phase current of 8 A. The line current magnitude is approximately?

A4.62 A
B8 A
C13.86 A
D24 A

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Correct Answer: C. 13.86 A

Explanation: For a balanced delta connection, IL=sqrt(3)Iph≈1.732×8=13.86 A.

Reference: Standard network theory: delta line current numerical

Question 1696

Network TheoryThree-Phase Circuits

A balanced three-phase system supplies 10 kW at 400 V line voltage and unity power factor. The line current is closest to?

A8.33 A
B14.43 A
C25 A
D43.3 A

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Correct Answer: B. 14.43 A

Explanation: P=sqrt(3)VLILcos(phi). At unity power factor, IL=10000/(1.732×400)≈14.43 A.

Reference: Standard network theory: three-phase current numerical

Question 1697

Network TheoryThree-Phase Circuits

A balanced three-phase load takes 6 kW at a power factor of 0.6 lagging. Its reactive power is?

A3.6 kVAR
B4.8 kVAR
C6 kVAR
D8 kVAR

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Correct Answer: D. 8 kVAR

Explanation: For cos(phi)=0.6, sin(phi)=0.8 and tan(phi)=4/3. Hence Q=P tan(phi)=6×4/3=8 kVAR.

Reference: Standard network theory: three-phase reactive power

Question 1698

Network TheoryThree-Phase Circuits

In the two-wattmeter method for a balanced three-phase load, total real power is equal to?

AW1-W2
BW1+W2
Csqrt(3)(W1+W2)
D3(W1-W2)

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Correct Answer: B. W1+W2

Explanation: For a balanced three-phase load measured by the two-wattmeter method, total real power is the algebraic sum W1+W2.

Reference: Standard network theory: two-wattmeter method

Question 1699

Network TheoryThree-Phase Circuits

In the two-wattmeter method, if the balanced load has unity power factor, the two wattmeters ideally read?

AEqual positive values
BEqual and opposite values
COne zero and one positive value
DBoth zero

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Correct Answer: A. Equal positive values

Explanation: At unity power factor phi=0, the readings are proportional to cos(30°-phi) and cos(30°+phi), so they are equal and positive.

Reference: Standard network theory: two-wattmeter unity power factor

Question 1700

Network TheoryThree-Phase Circuits

In the two-wattmeter method for a balanced load, one wattmeter reads zero when the power factor is?

A1
B0.866
C0.5
D0

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Correct Answer: C. 0.5

Explanation: One reading becomes zero at phi=60°, for which cos(phi)=0.5.

Reference: Standard network theory: two-wattmeter power factor